How to extrude and scale with an even offset?
Using "Inset" is a method to do this.

Select the face to "extrude", then press I to inset.

You can then inset a face almost like extruding and scaling, but evenly.



The inset tool is also useful for many other things, but this is one of its benefits.

Note: If you have a face that you would like to add a frame to, select the face then press I. You do not need to delete the face or anything. The "inset" tool is designed to inset :P